Problem: Solve for $x$ and $y$ using substitution. ${-5x+6y = 12}$ ${y = x+1}$
Solution: Since $y$ has already been solved for, substitute $x+1$ for $y$ in the first equation. ${-5x + 6}{(x+1)}{= 12}$ Simplify and solve for $x$ $-5x+6x + 6 = 12$ $x+6 = 12$ $x+6{-6} = 12{-6}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {y = x+1}\thinspace$ to find $y$ ${y = }{(6)}{ + 1}$ $y = 7$ You can also plug ${x = 6}$ into $\thinspace {-5x+6y = 12}\thinspace$ and get the same answer for $y$ : ${-5}{(6)}{ + 6y = 12}$ ${y = 7}$